Multiphase elasto-plastic mean-field homogenisation and its consistent linearisation

Abstract

The aim of this work is to develop a model based on incremental mean-field homogenisation methods that allows the simulation of composites with an arbitrary number of elasto-plastic material phases. The model is implemented in an implicit finite-element program, whereby, both matrix and inhomogeneities exhibit elasto-plastic material behaviour. Moreover, the implementation of the resulting constitutive equations is based on a consistent linearisation using higher order tensors. The proposed homogenisation method is evaluated by comparing it with existing methods from the literature in the context of two metal matrix composites. The target results used for comparison are obtained through computational homogenisation using FEM, taken from the literature. The overall findings indicate that the developed Mori-Tanaka method yields favourable results when compared to the existing approaches from the literature. Furthermore, a macroscopic tensile specimen with different microscopic morphologies is simulated using FEM and various mean-field homogenisation methods, including Mori-Tanaka, Voigt, Reuss, and Voigt-Reuss-Hill average. This example illustrates how the different microscopic morphologies and homogenisation methods influence the macroscopic response. Additionally, it demonstrates the successful implementation and correct linearisation of the proposed homogenisation method.